passive flow control for aerodynamic performance

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Ocean Engineering

journal homepage: www.elsevier.com/locate/oceaneng

Passive flow control for aerodynamic performance enhancement of airfoilwith its application in Wells turbine – Under oscillating flow condition

Ahmed S. Shehataa,b,⁎, Qing Xiaoa, Khalid M. Saqrc, Ahmed Naguibb, Day Alexandera

a Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow G4 0LZ, UKb Marine Engineering Department, College of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, P.O. 1029AbuQir, Alexandria, Egyptc Mechanical Engineering Department, College of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, P.O. 1029AbuQir, Alexandria, Egypt

A R T I C L E I N F O

Keywords:Sinusoidal flowWells turbinePassive flow control methodEntropy generationStall regimeLarge Eddy simulation

A B S T R A C T

In this work, the passive flow control method was applied to improve the performance of symmetrical airfoilsection in the stall regime. In addition to the commonly used first law analysis, the present study utilized anentropy generation minimization method to examine the impact of the flow control method on the entropygeneration characteristics around the turbine blade. This work is performed using a time-dependent CFD modelof isolated NACA airfoil, which refers to the turbine blade, under sinusoidal flow boundary conditions, whichemulates the actual operating conditions. Wells turbine is one of the most proper applications that can beapplied by passive flow control method because it is subjected to early stall. Additionally, it consists of a numberof blades that have a symmetrical airfoil section subject to the wave condition. It is deduced that with the use ofpassive flow control, torque coefficient of blade increases by more than 40% within stall regime and by morethan 17% before the stall happens. A significantly delayed stall is also observed.

1. Introduction

The techniques developed to maneuver the boundary layer, eitherfor the purpose of increasing the lift or decreasing the drag, areclassified under the general heading of boundary layer control or flowcontrol. In order to achieve separation postponement, methods of flowcontrol lift enhancement and drag reduction have been considered. It isimportant to note that flow control can be defined as a process used toalter a natural flow state or development path (transient betweenstates) into a more desired state (or development path; e.g. laminar,smoother, faster transients) (Collis et al., 2004). Moreover, it could bemore precisely defined as modifying the flow field around the airfoil toincrease lift and decrease drag. This could be achieved by usingdifferent flow control techniques such as blowing and suction, morph-ing wing, plasma actuators, and changing the shape of the airfoil(Katam, 2005). All the techniques essentially do the same job, i.e.reduce flow separation so that the flow is attached to the airfoil and,thus, reduce drag and increase lift. In regards to flow controltechniques, they can be broadly classified as active and passive flow

control which can be further classified into more specific techniques(Gad-el-Hak et al., 1998). The terms “active” or “passive” do not haveany clearly accepted definitions, but nonetheless are frequently used.Typically, the classification is based on energy addition, either on thepossibility of finding parameters and modifying them after the systemis built, or on the steadiness of the control system; whether it is steadyor unsteady. Such studies have demonstrated that suction slot canmodify the pressure distribution over an airfoil surface and have asubstantial effect on lift and drag coefficients (Yousefi et al., 2014;Chapin and Benard, 2015; Schatz et al., 2007; Chawla et al., 2014;Fernandez et al., 2013; Volino et al., 2011). A wide variety of differentstudies have been conducted on flow control techniques. In actual fact,in 1904, Prandtl (Schlichting, 1968) was the first scientist whoemployed boundary layer suction on a cylindrical surface to delayboundary layer separation. The earliest known experimental works onboundary layer suction for wings were conducted in the late 1930s andthe 1940s (Richards and Burge, 1943; Walker and Raymer, 1946;Braslow, 1999). Huang et al. (2004) studied the suction and blowingflow control techniques on a NACA0012 airfoil. The combination of jet

http://dx.doi.org/10.1016/j.oceaneng.2017.03.010Received 28 September 2016; Received in revised form 1 March 2017; Accepted 10 March 2017

⁎ Corresponding author at: Marine Engineering Department, College of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, P.O. 1029AbuQir, Alexandria, Egypt.

E-mail address: [email protected] (A.S. Shehata).

Abbreviations: CFD, Computational Fluid Dynamics; NACA, National Advisory Committee for Aeronautics; OWC, Oscillating Water Column; 2D, Two Dimensional; 3D, ThreeDimensional

Ocean Engineering 136 (2017) 31–53

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location and angle of attack showed a remarkable difference concerninglift coefficient as perpendicular suction at the leading edge increased incomparison to the case in other suction situations. Moreover, thetangential blowing at downstream locations was found to lead to themaximum increase in the lift coefficient value. Rosas (2005) numeri-cally studied flow separation control through oscillatory fluid injection,in which lift coefficient increased. The authors in Akcayoz and Tuncer(2009) examined the optimization of synthetic jet parameters on aNACA0015 airfoil in different angles of attack to increase the lift todrag ratio. Their results revealed that the optimum jet location movedtoward the leading edge and the optimum jet angle incremented as theangle of attack increased. The CFD method has been increasingly usedto investigate boundary layer control. Many flow control studies byCFD approaches (Kim and Kim, 2009; Genc et al., 2011; Rumsey andNishino, 2011; Yagiz et al., 2012) have been conducted to investigatethe effects of blowing and suction jets on the aerodynamic performanceof airfoils.

The major challenge facing oscillating water column ocean energyextraction systems is to find an efficient and economical means ofconverting flow kinetic energy to unidirectional rotary motion fordriving electrical generators (Rosa, 2012; Curran and Folley, 2008;Falcao, 1999, 2004; Torres et al., 2016), as seen in Fig. 1. The energyconversion from the oscillating air column (Boccotti, 2007a, 2007b)can be achieved by using a self-rectifying air turbine such as Wellsturbine which was invented by Wells in 1976, see Fig. 2 (Raghunathan,1980; Hitoshi Hotta, 1985; Masahiro Inoue et al., 1985; MasamiSuzuki and Tagori, 1985; Yukihisa Washio et al., 1985; Folley et al.,2006). Wells turbine consists of a number of blades that havesymmetrical airfoil section. This airfoil section under different condi-tions with various geometric parameters was investigated by otherresearchers in consideration of improving the overall system perfor-mance. In order to achieve this purpose, different methods were used,such as experimental, analytical and numerical simulation. The maindisadvantage of Wells turbine is the stall condition (Shehata et al.,2017b). Aerodynamic bodies subjected to pitching motions or oscilla-tions exhibit a stalling behavior different from that observed when theflow over a wing at a fixed angle of attack separates. The latterphenomenon is referred to as static stall, since the angle of attack isfixed. In the case of a dynamically pitching body, such as an airfoil withlarge flow rates and a large angle of attack, the shear layer near theleading edge rolls up to form a leading-edge vortex which providesadditional suction over the upper airfoil surface as it convects down-

stream. This increased suction leads to performance gains in lift andstall delay, but the leading-edge vortex quickly becomes unstable anddetaches from the airfoil. As soon as it passes behind the trailing edge,however, the leading-edge vortex detachment is accompanied by adramatic decrease in lift and a significant increase in drag. Thisphenomenon is called dynamic stall. From Fig. 3 it can be noted thatWells turbine can extract power at low air flow rate, when otherturbines would be inefficient (Liu et al., 2016; Okuhara et al., 2013).Also, the aerodynamic efficiency increases with the increase of the flowcoefficient (angle of attack) up to a certain value, after which itdecreases. Thus, most of the past studies aimed to 1) improve thetorque coefficient (the turbine output) and 2) improve the turbinebehavior under the stall condition. In a number of previous studies(Raghunathan, 1995a; Dixon, 1998; Sheldahl and Klimas, 1981), it wasconcluded that the delay of stall onset contributes to improving Wellsturbine performance. This delay can be achieved by setting guide vaneson the rotor's hub (Raghunathan, 1995a, 1995b; Brito-Melo et al.,2002). It was found that a multi-plane turbine without guide vanes wasless efficient (approximately 20%) than the one with guide vanes. Acomparison between Wells turbines having 2D guide vanes and 3Dguide vanes was investigated (Setoguchi et al., 2001; Takao et al., 2001)by testing a Wells turbine model under steady flow conditions, andusing the computer simulation (quasi-steady analysis. It demonstratedthat, the 3D case has superior characteristics in the running andstarting characteristics. Concerning Wells turbine systems which

Nomenclature

A The total blade area (m2)c Blade chord (m)CD Drag force coefficientCL Lift force coefficientCT Torque coefficientD The fluid domainDss Suction slot diameter (m)f Cycle frequency (Hz)FD In-line force acting on cylinder (N)G The filter functionKE Kinetic Energy (J)Lss Suction slot location from leading edge in chord percen-

tage %K Turbulent kinetic energy (J/kg)Δp Pressure difference across the turbine (N/m2)Rm Mean rotor radius (m)Sgen Local entropy generation rate (W/m2 K)SG Global entropy generation rate (W/K)Sij Mean strain rate (1/s)

St Thermal entropy generation rate (W/m2 K)SV Viscous entropy generation rate (W/m2 K)To Reservoir temperature (K)U Moving frame velocity (m/s)ui Reynolds Averaged velocity component in i direction (m/

s)V Volume of a computation cell (m3)Va Instantaneous Velocity (m/s)Vam Highest speed of axial direction (m/s)Vo Initial velocity for computation (m/s)Vr Relative velocity (m/s)W The net-work transfer rate (W/s)Wrev Reversible work transfer rate (W/s)ηF The efficiency in first law of thermodynamicsηS The second law efficiencyμ Viscosity (kg/m s)μt Turbulent viscosity (N s/m2)ρ Density (kg/m3)∅ Flow coefficientω Rotor angular speed (rad/s)

ρu u(− ′ ′)i j Reynolds stress tensor

Fig. 1. An illustration of the principle of operation of OWC system, where the wavemotion is used to drive a turbine through the oscillation of air column (Takao et al.,2001).

A.S. Shehata et al. Ocean Engineering 136 (2017) 31–53

32

operate at high pressure values, a multi plane (usually tow stage)turbine configuration can be used. Such a concept avoids the use ofguide vanes and, therefore, the turbine would require less maintenanceand repairs (Raghunathan, 1995a). The performance of a biplane Wells

turbine is dependent on the gap between the planes as it is shown inRaghunathan (1995a). A gap-to-chord ratio between the planes of 1.0was recommended. Experimental results in Gato and Curran (1996)showed that the use of two twin rotors rotating in the oppositedirection to each other was an efficient means of recovering the swirlkinetic energy without the use of guide vanes. The overall performanceof several types of Wells turbine design have been investigated inRaghunathan and Beattie (1996) and, a semi-empirical method forpredicting the performance has been used in Curran et al. (1998).Similar comparisons were undertaken using experimental measure-ment in Gato and Curran (1997). It can be observed that the contra-rotating turbine had an operational range which was similar to that ofthe monoplane turbine with guide vanes and it achieved similar peakefficiency as well. However, the flow performed was better than thelatter in the post-stall regime. In order to improve the performance ofthe Wells turbine, the effect of end plate on the turbine characteristicshas been investigated in Mamun et al. (2006), Takao et al. (2007).Using an experimental model and a CFD method it was shown that theoptimum plate position was a forward type. The peak efficiencyincreases approximately 4% as compared to the Wells turbine withoutan endplate. The calculations of the blade sweeps for the Wells turbinewith a numerical code by Kim et al. (2002) and experimentally withquasi-steady analysis in Setoguchi et al. (2003a). As a result, it wasconcluded that the performance of the Wells turbines was influenced bythe blade sweep area.

Exergy analysis is performed using the numerical simulation forsteady state biplane Wells turbines (Shaaban, 2012) where the up-stream rotor has a design point second law efficiency of 82.3% althoughthe downstream rotor second law efficiency equals 60.7%. The entropygeneration, due to viscous dissipation, around different 2D airfoilsections for Wells turbine was recently examined by the authors inShehata et al. (2014, 2016). When Reynolds number was increasedfrom 6×104 to 1×105 the total entropy generation increased more thantwo folds for both airfoils correspondingly. However, when Reynoldsnumber was increased further to 2×105, the total entropy generationexhibited unintuitive values ranging from 25% less to 20% higher thanthe corresponding value at Reynolds number=1×105. The efficiency forfour different airfoils in the compression cycle is higher than thesuction cycle at 2° angle of attack. Although, when the angle of attackincreases, the efficiency for the suction cycle increases much more thanthe compression one. This study suggested that a possible existence ofcritical Reynolds number for the operating condition at which viscousirreversibilities takes minimum values. A comparison between totalentropy generation of a suggested design (with variable chord) and aconstant chord of Wells turbine was presented in Soltanmohamadi andLakzian (2015). The detailed results demonstrate an increase in staticpressure difference around a new blade and a 26.02% average decreasein total entropy generation throughout the full operating range. Most ofthe researchers studied the performance of different airfoils design anddifferent operational conditions where analyzing the problem was onlybased on the parameter of first law of thermodynamics. In order toform a deeper understanding, it is necessary to look at the second lawof thermodynamics since it has shown very promising result in many

Fig. 2. Typical structure of Wells turbine rotor (Takao et al., 2001).

Fig. 3. Turbines characteristic under steady flow conditions: Flow coefficient variationwith the efficiency (Akcayoz and Tuncer, 2009).

Fig. 4. Computational model and boundary conditions A) dimensions of wholecomputational domain and location of airfoil B) computational grid near the wall ofthe airfoil.

Fig. 5. The near views of slot mesh A) DSS=0.005 m B) DSS=0.001 m.


33

applications, such as wind turbine in Pope et al. (2010), Baskut et al.(2010, 2011), Redha et al. (2011), Ozgener and Ozgener (2007),Mortazavi et al. (2015), and gas turbine in Şöhret et al. (2015),Ghazikhani et al. (2014), Sue and Chuang (2004), Kim and Kim(2012), Jubeh (2005), Lugo-Leyte et al. (2015).

Wells turbine consists of a number of blades that have symmetricalairfoil section. This airfoil section under different conditions withvarious geometric parameters was investigated by other researchersto improve the overall system performance. Different methods wereused to achieve this purpose, such as experimental, analytical andnumerical simulation. In this work the CFD analysis is used toinvestigate and analyze the flow around the isolated NACA airfoil,which refers to the turbine blade, under sinusoidal flow boundaryconditions, which emulates the actual operating conditions. The forcecoefficients, such as torque coefficient and the entropy generation

value, are calculated and compared under different conditions withvarious design parameters by analyzing the flow around the airfoilsection using CFD software, where the force coefficients are referring tothe first law analysis and the entropy generation value is referring tothe second law analysis. The objective of the present work is todemonstrate that the performance of airfoil section, which refers tothe Wells turbine blade at stall and near-stall conditions, can beradically improved by using passive flow control method such as

Fig. 6. Convergence criteria A) non-oscillating flow B) sinusoidal flow.

Fig. 7. The sinusoidal wave boundary condition, which represents a regular oscillatingwater column.

Fig. 8. A grid sensitivity analysis with respect to cell number across the slot section A)one, two, four and eight cells in the transversal direction B) pressure coefficient plottedon the normalized aerofoil cord at different grid resolutions.


34

suction or blowing slot. Therefore, a typical slot is created in the airfoilsection, normal to the chord, and due to the pressure differencebetween the two surfaces. Consequently, a suction effect occurs whichdelays the stall. Accordingly, there is no need to generate any specificactive suction or blowing within the airfoil or the slot. Along with thisdesign, there are two new aspects here. The first is improving theperformance of airfoil section for Wells turbine in near-stall conditions.The second is to study the effect of slot in oscillating (i.e. sinusoidal)flow, which is newly compared to the unidirectional flow as inaerodynamics applications. Apart from that, an entropy generationminimization method is used to conduct the second-law analysis asrecently reported by the authors in Shehata et al. (2014, 2016). Aninvestigation on the entropy generation, due to viscous dissipation,around turbine airfoils in two-dimensional unsteady flow configura-tions, will be carried out. In reference to the literature, no specificunsteady CFD study of the slot effect with sinusoidal flow on theentropy generation rate has been performed for airfoil section of Wellsturbine.

2. Mathematical model and numerical approach

The governing equations employed for Large Eddy Simulation(LES) are obtained by filtering the time-dependent Navier-Stokesequations. The filtering process effectively filters out eddies whosescales are smaller than the filter width or grid spacing used in thecomputations. The resulting equations thus govern the dynamics oflarge eddies. A filtered variable (denoted by an over-bar) is definedby SB (2000):

∫ϕ x ϕ x G x x dx( ) = ( ′) ( , ′) ′D (1)

where D is the fluid domain, and G is the filter function that determines

the scale of the resolved eddies. In FLUENT, the finite-volumediscretization itself implicitly provides the filtering operation(Mamun, 2006):

∫ϕ xV

ϕ x dx x V( ) = 1 ( ′) ′, ′∈V (2)

where V is the volume of a computational cell. The filter function, G (x,x′), implied here is then

⎧⎨⎩G x x V for x Votherwise

( , ′) = 1/ ′∈0 (3)

The LES model will be applied to essentially incompressible (butnot necessarily constant-density) flows. By filtering the incompressibleNavier-Stokes equations, one obtains (Dahlstrom, 2003)

ρt

ρux

∂∂

+ ∂∂

= 0i

i (4)

⎛⎝⎜

⎞⎠⎟t

ρux

ρu ux

μ ux

ρx

τx

∂∂

( ) + ∂∂

( ) = ∂∂

∂∂

− ∂∂

−∂∂i

ji j

j

i

j i

ij

j (5)

where τij is the sub-grid-scale stress defined by

τ ρu u ρu u= −ij i j i j (6)

The sub-grid-scale stresses resulting from the filtering operation areunidentified, and require modeling. The majority of sub-grid-scalemodels are eddy viscosity models of the following form (Moin et al.,1991):

τ τ σ μ S− 13

= −2ij kk ij t ij (7)

where Sij is the rate-of-strain tensor for the resolved scale defined by:

⎛⎝⎜

⎞⎠⎟S u

xux

= 12

∂∂

+∂∂ij

i

j

j

i (8)

and μt is the sub-grid-scale turbulent viscosity, which the Smagorinsky-Lilly model is used for it (DK, 1992). The most basic of sub-grid-scalemodels for “Smagorinsky-Lilly model” was proposed by Smagorinsky(Hinze, 1975) and was further developed by Lilly (Launder andSpalding, 1972). In the Smagorinsky-Lilly model, the eddy viscosityis modeled by:

μ ρL S=t s2 (9)

where Ls is the mixing length for sub-grid-scale models andS S S= 2 ij ij . The Ls is computed using:

L kd C V= min ( , )s s1/3 (10)

where Cs is the Smagorinsky constant, k = 0.42, d is the distance to theclosest wall, and V is the volume of the computational cell. Lilly deriveda value of 0.23 for Cs from homogeneous isotropic turbulence.However, this value was found to cause excessive damping of large-scale fluctuations in the presence of mean shear or in transitional flows.Cs=0.1 has been found to yield the best results for a wide range of flows.

For the first law of thermodynamics, the lift and drag coefficient CL

and CD are computed from the post processing software. The averagevalue for lift and drag coefficient was used to calculate one value fortorque coefficient for each angle of attack. Afterwards, the torquecoefficient can then be expressed as (Sheldahl and Klimas, 1981;Curran et al., 1998; Whittaker et al., 1997):

C C sinα C α= ( − cos )T L D (11)

The flow coefficient ϕ relating tangential and axial velocities of therotor is defined as

ϕ Vω R

=*

a

m (12)

where the α angle of attack equal to

Fig. 9. The measure of LES quality by M(x, t) with the sub-grid filter length.

Fig. 10. A histogram of number of elements for the sub-grid filter length.


35

α tan VωR

= a

m

−1(13)

and the torque as:

Torque ρ V ωR AR C= 12

( +( ) )a m m T2 2

(14)

the efficiency in the first law of thermodynamics (ηF) is defined as:

η Torque ωΔP Q

= **F (15)

The transport equations of such models can be found in turbulencemodeling texts such as Hirsch (2007). The second law of thermo-dynamic defines the network transfer rate W as Bejan (1996):

W W T S − =rev o gen (16)

Which has been known for most of this century in engineering as

the Gouy–Stodola theorem (Stodola, 1910).It is possible to express the irreversible entropy generation in terms

of the derivatives of local flow quantities in the absence of phasechanges and chemical reactions. The two dissipative mechanisms inviscous flow are the strain-originated dissipation and the thermaldissipation which correspond to a viscous and a thermal entropygeneration respectively (Iandoli, 2005). Thus, it can be written,

S S S= +gen V th (17)

In incompressible isothermal flow, such as the case in hand, thethermal dissipation term vanishes. The local viscous irreversibilitiestherefore can be expressed as:

S μT

ϕ=Vo (18)

where ϕ is the viscous dissipation term, that is expressed in two

Fig. 11. Comparison between different models to simulate the stall angle from experimental data A) torque coefficient B) path-line colored by the velocity magnitude C) contours ofpressure distribution D) pressure distribution at upper and lower surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version ofthis article.)


36

dimensional Cartesian coordinates as Iandoli (2005):

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

⎛⎝⎜

⎞⎠⎟ϕ u

xvy

uy

vx

= 2 ∂∂

+ ∂∂

+ ∂∂

+ ∂∂

2 2 2

(19)

Eqs. (18) and (19) were used to create the UDF file, which is used tocalculate the local entropy form the FLUENT software. Then, the globalentropy generation rate is hence expressed as:

∬S S dydx=Gxy

V(20)

Which is also calculated from the FLUENT software by integral theglobal value,

The next equation is defining the exergy value, which can be writtenas Bejan (1995):

Exergy KE S= + G (21)

and finally the second law efficiency is defined as Pope et al. (2010):

η KEExergy

=S (22)

Fig. 11. (continued)


37

where KE V= 12

2

From the above equation we can come up with a number ofconclusions. On the one hand, that the torque coefficient indicates tothe first law efficiency and the global entropy generation rate indicatesto the second law and efficiency, in which the increase in torquecoefficient leads to increase in the first law efficiency. On the otherhand, the decrease in the global entropy generation rate leads to anincrease in the second law efficiency.

3. CFD approach

3.1. Computational model, solver details and boundary conditions

Two-dimensional numerical models for NACA0015 airfoils werebuilt and validated against experimental measurements under unstea-dy flow conditions with both non-oscillating velocity, and sinusoidalinlet velocity. The computational domain is discretized to Cartesianstructured finite volume cells using GAMBIT code. The application ofsuch boundary condition types (Starzmann and Carolus, 2013;Mohamed and Shaaban, 2013; Torresi et al., 2009; Mamun et al.,2004) matches the Green-Gauss cell based evaluation method for thegradient terms used in the solver (ANSYS FLUENT). Numerous testsaccounting for different interpolation schemes were used to computecell face values of the flow field variables. The variables of governingequation which are velocity and pressure, as well as convergence testshave been undertaken. The second order upwind (Smagorinsky, 1963)interpolation scheme was used in this work in which it yields resultswhich are approximately similar to such yielded by third order MUSCLscheme in the present situation. In addition, in some cases of the thirdorder MUSCL scheme was given high oscillatory residual during thesolution. Fig. 4 demonstrates the dimensions of the whole computa-tional domain and the location of airfoil, and it also shows the griddistribution near the wall of the airfoil. Furthermore, the near views ofslot mesh can be determined from Fig. 5 for different slot diameter. TheQuad-Pave meshing scheme (Structured Grid) is used in this work. It

was also detected that the solution reaches convergence when thescaled residuals approaches 1×10−5. See Fig. 6 for the convergencecriteria in the non-oscillating flow and sinusoidal flow inlet velocity. Atsuch limit, the flow field variables holds constant values with theapplication of consecutive iterations.

The axial flow of Wells Turbine is modeled as a sinusoidal wave inthis simulation. Therefore, Inlet boundary conditions are set to changeas time. In order to apply the inlet boundary condition, inlet velocitywith periodic function (see Fig. 7) is generated as follows.

V V V sin πft= + (sin 2 )a o am (23)

Where t is time period, 6 s are set as one period in this simulationconsidering to the literature survey (Mamun et al., 2004; Setoguchiet al., 2003b; Kinoue et al., 2003a, 2004). Time step is set as0.000296721 s in order to satisfy CFL (Courant Friedrichs Lewy) (DEMoura and Carlos, 2013) condition equal to 1. The sinusoidal wavecondition create various Reynolds number up to 2×104 according to theRef. Torresi et al. (2009).

Fig. 12. Measured torque coefficient from Refs. Torresi et al. (2007b, 2007a, 2009) andcalculated torque coefficient from present CFD unsteady flow with non-oscillatingvelocity.

Table 1The error percentage between measured torque coefficient from Refs. Torresi et al. (2007b, 2007a, 2009) and calculated torque coefficient from CFD under unsteady flow with non-oscillating velocity.

Torque Coefficient Angle of attack (Degree)

8.709 10.097 10.639 11.266 11.734 12.304 13.642 14.406

Experimental 0.0488 0.0631 0.0712 0.0807 0.0875 0.0922 0.0814 0.0725CFD 0.05092 0.06689 0.0726 0.0793 0.0856 0.091 0.083 0.0676Error % 4 6 2 −2 −2 −1 2 −7

Fig. 13. Measured unsteady in-line force FD from Ref. Nomura et al. (2003), (angle of

attack=0°) and FD calculated from the present CFD for frequency 2 Hz.

Fig. 14. Measured unsteady in-line force FD from Ref. Nomura et al. (2003), (angle of

attack=0°) and FD calculated from the present CFD for frequency 1 Hz.


38

3.2. Grid sensitivity test

In order to ensure that the numerical produces results are mini-mally dependent on the grid size, several grids were tested to estimatethe number of grid cells required to establish a reliable model. The gridsensitivity test is performed where 4 grids with different mesh sizesranging from 112603 up to 446889 cells are investigated. This testshows that for grids with mesh sizes of 312951 cells, gives good resultwithin reasonable computation time (more details about this resultin Shehata et al. (2014)). Therefore, it was selected to conduct theanalysis presented hereafter.

Fig. 8 show the grid sensitivity analysis with respect to cell number

across the slot section for one, two, four and eight cells in thetransversal direction. It can be noted that the results for the four gridsA–D are approximately the same. On the other hand, by increase thenumber of cells in the transversal direction, the cells number for thetotal domain is increase for the four grids A–D by 312951, 350662,388637 and 413665 respectively. Therefore, the grid A was selected inorder to immunize the solution time of the different cases withoutimpacting on the quality and accuracy of the results.

3.3. LES resolution quality assessment

In the most common practice, in LES, the filter length depends onthe resolution of spatial discretization (i.e. grid) in a specified problem.The implication of the filtering technique, which is the backbone ofLES, is the question about the resolution of the resolved scales incomparison with the total turbulence spectrum in the flow. Anassortment of several attempts were made to propose and index ofLES quality (Saqr, 2010; Celik et al., 2005). The most established indexof LES quality was proposed by Pope (Pope, 2004). Such quality indexcan be expressed mathematically as a function M x t( , ) of space andtime (Saqr et al., 2012) as:

M x t KK K

( , ) =+Res

Res SGS

where KRes and KSGS are the resolved and subgrid modeled turbulentkinetic energy scalars, respectively. In the present work, KRes can becalculated as: K u v= ( + )∼ ∼

Res12

2 2 and KSGS can be calculated as

K =SGSν

C( Δ)t2

2 where νt is the subgrid modeled turbulent kinematic

viscosity as calculated in the Smagorinsky model as: ν L S=t s2 , where

LS is the mixing length for subgrid scales as calculated in Eq. (10) and Δis the filter length (Eldrainy et al., 2011). Pope (2004) has evidentlyshown that when M x t( , )≥80% the LES is sufficiently resolved and theflow field is properly resolved. Literature records support Pope'sproposition in numerous and variant flows as reported in Mazzeiet al. (2016), Fureby (2017), Georgiadis et al. (2010), Eldrainy et al.(2011). In the present work, the quality index M x t( , ) was calculatedfor the computational domain and plotted against LES filter length asin Fig. 9. It is shown that M x t( , )≥80% for filter lengths in the range∆ ≥ 0.01. In Fig. 10 a histogram of the filter length shows thatapproximately 98% of the grid has values of M x t( , ) larger than 90%which satisfies Pope's criteria for fully resolved LES.

Since one of the work main objectives is to study the stall regime,therefore, an accurate simulation for the stall must be done. Thefollowing Fig. 11 illustrates that a comparison between differentmodels to simulate two dimensional NACA0015 in an unsteady flowwith stall angle (13.6°) for NACA0015 with Reynolds number equals to2×105 from experimental data (Torresi et al., 2009, 2007) waspresented. The comparison uses only the stall angle to identify whichmodel can present it. The Large Eddy Simulation model (LES) givesgood results for the torque coefficient value, while, other models cannot

Table 2The error percentage between measured FD from Ref. Nomura et al. (2003) and calculated FD from CFD under unsteady flow with sinusoidal inlet velocity.

FD*10−2 (N) Time (s)

14.02 14.1 14.12 14.2 14.3 14.34 14.4 14.5 14.6 14.7 14.8 14.9 15

Frequency 2 HzExperimental 3.3 7.6 9.7 14.1 12.7 3.3 4 2.3 7.4 14.4 10.5 3.8 2.6CFD 3.7 7.6 9.6 14.2 12.3 3.4 3.3 2.6 7.6 14.6 10.7 3.7 2.4Error % 11 1 −1 1 −4 1 −17 17 4 1 2 −2 −11

Frequency 1 HzExperimental 4.4 6.8 12.4 13.8 14 12.7 10 7.6 4.6 2.7 2.3 2.5 2.9CFD 4.5 7.1 12.4 12.9 14 12.9 10.1 8.4 4.4 2.6 2.2 2.6 3.2Error % 2 4 0 −7 0 1 1 10 −4 1 −4 4 10

Fig. 15. Measured torque coefficient from Refs. Torresi et al. (2007b, 2007a, 2009) andcalculated torque coefficient from CFD unsteady flow with sinusoidal inlet velocity.

Table 3The error percentage between measured torque coefficient from Refs. Torresi et al.(2007b, 2007a, 2009) and calculated torque coefficient from CFD under unsteady flowwith sinusoidal inlet velocity.


11.266 11.734 12.304 13.642 14.406

Experimental 0.0807 0.0875 0.092 0.0814 0.0725CFD 0.0803 0.0879 0.0931 0.0825 0.0709Error % −1 1 1 1 −2

Fig. 16. 2D airfoil diagram with a slot.


39

Fig. 17. Factors affecting determination of the slot velocity direction for the pressure distribution and velocity vector direction A) accelerating flow at compression cycle B) deceleratingflow at compression cycle C) accelerating flow at suction cycle D) decelerating flow at suction cycle.


40

predict the stall angle. The LES model has shown high disturbance forthe path line of the flow stream and the pressure distribution at theupper surface, which leads to the stall condition. The larger turbulentseparated zone of the LES may be a reason for the lower value of the liftforce (Richez et al., 2007). The LES has shown that some vortexes wereformed and caused to appear a fluctuation behavior of pressuredistribution on the upper surface of the airfoil, whereas other models

were not able to predict it (Rezaei et al., 2013). On the other hand, theunsteady RANS turbulence modeling has shown a quite dissipativecharacter that attenuates the instabilities and the vortex structuresrelated to the dynamic stall (Martinat et al., 2008). Therefore, the LESmodel will be used to investigate the stall behavior.

Large Eddy Simulation model was used to model the flow aroundNACA0015 airfoil in order to give the best agreement with experi-mental data adopted from Torresi et al. (2009, 2007) and Nomura et al.(2003). The Large Eddy Simulation model gives excellent results whenthey are used to simulate the airfoil in stall condition, according toliterature survey (Dahlstrom, 2003; Richez et al., 2007; Kawai andAsada, 2013; Alferez et al., 2013; Kim et al., 2015; AlMutairi et al.,2015; Armenio et al., 2010; Hitiwadi et al., 2013; Bromby, 2012).

Although LES is a 3D model by definition, there have beennumerous successful attempts to use it in 2D applications. Forexample, flow over obstacles (Skyllingstad and Wijesekera, 2004),hump (Avdis et al., 2009), block (Cheng and Porté-Agel, 2013), airfoils(Hitiwadi et al., 2013; Tenaud and Phuoc, 1997; Shehata et al., 2017a)and Hills (Chaudhari et al., 2014). Other two dimension modelapplications include the problems dealing with, dam-break(Özgökmen et al., 2007), mechanism of pollutant (Michioka et al.,2010; Chung and Liu, 2013), heat transfer (Andrej Horvata and Marnb,2001; Matos et al., 1999), turbulent Convection (Chen and Glatzmaier,2005) and Parallel Blade Vortex (Liu et al., 2012). The flow underinvestigation occurs due to sinusoidal velocity signal in the XY plane,with no other velocity signals in other domains. Hence, all the mainflow phenomena of interest occurs in the XY plane except for the vortexstretching and secondary shedding which occur in the XZ and YZplanes. The authors have reviewed the 2D assumption of the flow underconsideration in their recent extensive review paper (Shehata et al.,2017) and concluded that the 2D assumptions are not influential in theflow structure nor the aerodynamic performance of the airfoil underoscillating flow. Hence, the governing equations were reduced to twodimensional form, and solved accordingly. Consequently, and given thefact that this reduction is physically valid, the method of solution of thegoverning equation (i.e. LES) must follow the coordinate formalism ofthe governing equations, hence it was solved as two-dimensionalproblem. In this work two sets of experimental data were used tovalidate the numerical model from references. First, experimental datafrom Refs. Torresi et al. (2009, 2007) are used to simulate and validatethe stall condition. Details of the first validation case, where Wellsturbine prototype are under investigation, is characterized by thefollowing parameters: hub radius, is equal to101 mm; tip radius, equalto 155 mm; NACA0015 blade profile with constant chord length, equalto 74 mm; and number of blades, equal to 7. Therefore, the hub-to-tipratio, and the solidity, is equal to 0.65 and 0.64, respectively. Theuncertainty in the measurements is 5%. The blades have been producedwith composite material reinforced by carbon fiber with suited attach-ment. Second, experimental data from Ref. Nomura et al. (2003) isadopted to simulate and validate the unsteady sinusoidal wave inletvelocity. Details of the second validation case, where experimental datafor unsteady forces (FD) acting on a square cylinder in oscillating flowwith nonzero mean velocity are measured. The oscillating air flows aregenerated by a unique AC servomotor wind tunnel. The generated

Fig. 18. Torque coefficient for different Dss at stall angle.

Fig. 19. Torque coefficient for suction slots at different Lss at 13.64°.

Fig. 20. Suction slot with optimum Lss (45%) and optimum Dss (0.001 m) at different

angles of attack.

Table 4The improvement percentage between NACA0015 without suction slot and with suction slot at optimum Lss and Dss under unsteady flow with non-oscillating velocity.


8.709 10.097 10.639 11.266 11.734 12.304 13.642 14.406

Without Suction Slot 0.0509 0.0669 0.0726 0.0793 0.0856 0.091 0.083 0.0676D =0. 001ss m at L =45%ss 0.0568 0.0744 0.0776 0.091 0.1022 0.104 0.119 0.0977Improvement % 12 11 7 14 19 14 44 45


41

velocity histories are almost exact sinusoidal waves.For unsteady flow with non-oscillating velocity, Fig. 12 shows a very

good agreement between the measured torque coefficient from Refs.Torresi et al. (2009, 2007) and the calculated torque coefficient fromCFD result at Reynolds number of 200000. It can be noted that thecomputational model has approximately the same stall condition valueas the reference. The comparison between those results and thepercentage of error are listed in Table 1. Furthermore, for an unsteadyflow with sinusoidal inlet velocity, Figs. 13 and 14 show a goodagreement between measured drag force from Ref. Nomura et al.

(2003) and predicted drag force from CFD at two different frequencies(2 Hz and 1 Hz). It can be shown from Figs. 13 and 14 that thecomputational model has almost the same behavior of oscillating flowcondition as the reference; see also the error percentage in Table 2 forthe two frequencies. Finally, Fig. 15 displays the results of computa-tional model under sinusoidal inlet flow velocity with experimentaldata from Torresi et al. (2009, 2007) and an excellent agreement isachieved. The comparison of these results and the percentage of errorare summarized in Table 3. The Large Eddy Simulation computationalmodel has approximately the same stall condition value as the

Fig. 21. The path-line for mean velocity magnitude at certain velocity equal to 2.92 m/s unsteady input flow with non-oscillating velocity, a) and b) 12.3°, c) and d) 13.6°, e) and f)14.4°. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Fig. 22. The pressure coefficient around the airfoil, unsteady input flow with non-oscillating velocity, A) and B) 12.3°, C) and D) 13.6°, E) and F) 14.4°.


42

reference.

4. Results and discussion

A slot with certain diameter at various locations from the leading

edge was created with a shape of NACA0015 from Refs. Torresi et al.(2009, 2007), see Fig. 16. The diameter and location for the slot werechanged in order to obtain an optimum value. During the compressioncycle, this slot suctions the flow from lower surface (high pressure) andblows it to the upper surface (low pressure), see Fig. 17. Where,Fig. 17A is for the accelerating flow at 1.3 s and B is for the deceleratingflow at 1.65 s with Reynolds number equal to 190000. Furthermore,this pressure difference affecting on the velocity vector direction, as itcan be noted in Fig. 17 for the velocity vector of the velocity magnitude.On the other hand, during the suction cycle in Fig. 17C (4.35 s) and D(4.6 s), the slot suctions the flow from the upper surface (high pressure)and blows it to the lower surface (low pressure) in both the acceleratingand decelerating flow at Reynolds number equal to 190000. It can bealso noted that the pressure difference affecting on the velocity vectordirection, which it refer to the flow direction. Therefore, it can beconcluded that the factor affecting determination of the slot velocitydirection is the pressure difference. The slot will be defined as a suctionslot in the analysis and results which were presented henceforth. Thetest cases investigated are under 1) unsteady flow with non-oscillatingvelocity and 2) sinusoidal wave condition.

Fig. 23. Pressure coefficient distribution on the upper and lower surface of the airfoil, A) and B) 12.3°, C) and D) 13.6°, E) and F) 14.4°.

Fig. 24. The effect of suction slot on the global entropy generation rate with differentangle of attack.


43

4.1. Unsteady flow with non-oscillating velocity

The effect of suction slots in the airfoils behavior will be shown inthe following three sections.

4.1.1. Torque coefficient and Stall angleFig. 18 demonstrates the effect of varying Dss on the torque

coefficient at the stall angle (13.6°) from Fig. 11 for Refs. Torresi et al.(2009, 2007). All suction slots have Lss up to 65%. It can be remarkedthat the suction slot with Dss of 0.001 m gives a higher torquecoefficient than others. The torque coefficient increases about 26%than the airfoil without suction slot.

Fig. 19 exemplifies the effect of Lss on the torque coefficient at thestall angle (13.6°) with Dss equal to 0.001 m. It can be discerned that,the Lss equal to 45%, gives a higher torque coefficient than other Lss.Where, the torque coefficient increases about 42% than the airfoilwithout suction slot.

Fig. 20 reveals the effect of suction slot with optimum Lss andoptimum Dss on the torque coefficient at different angles. It is clearlynoted that the improvement of torque coefficient at different angles(from 7% to 19%), especially at stall regime (from 44% to 45%), whichis caused by the delay in stall angle. For more details about the value ofimprovement in torque coefficient, see Table 4.

4.1.2. Flow field around the airfoil sectionFig. 21 shows path lines colored by mean velocity magnitude at

maximum value of torque coefficient and stall condition. In addition, italso shows the effect of suction slot on the boundary layer and flow fieldaround the airfoil. Also, it highlights the amount of the differencebetween the effects of suction slot before and after the stall condition.This difference is clearly indicated between Fig. 21a, b for 12.3° and c,d for 13.6°. The effect of suction slot on the separation layer at the endof blade in Fig. 21a, b was small. This is due to the fact that the towFigure did not have the stall condition yet. On the other hand, the effectof suction slot on the separation layer in Fig. 21c and d is significantbecause Fig. 21c represents the data in the stall condition however,Fig. 21d does not. As for Figures e and f, the two airfoils are in stallregime. Figs. 22 and 23 clarify the pressure distribution around theupper and lower surface of airfoil at maximum velocity (2.92 m/s) withdifferent angles of attack. It can be shown that the low pressure area atthe trailing edge was increased with the increase in angle of attack forthe airfoil without slots. From Fig. 23A), C) and E) it can be noted thatthe low pressure zones and disturbances at the trailing edge for theupper surface was created the layer separation at the trailing edge andit was also increased by the increase in angle of attack. The effect of thesuction slot was very clear at the pressure distribution around theairfoil, where it was more significant after the stall angles (13.6 and14.4°) than that before the stall (12.3°). The difference between thepressure value for the upper and lower surface at the trailing edge wasdecreased by adding suction slot to the airfoil especially at the stallangles.

Fig. 25. a) Suction slot with Dss equal to 0.001 m at different Lss for instantaneous

torque coefficient at 13.6° under unsteady flow with sinusoidal inlet velocity b) suctionslot with Dss equal to 0.001 m at different Lss for average torque coefficient at 13.6° under

unsteady flow with sinusoidal inlet velocity.

Fig. 26. Suction slot with optimum Lss (45%) and optimum Dss (0.001 m) at different

angles of attack under unsteady flow with sinusoidal inlet velocity.

Table 5The improvement percentage between NACA0015 without suction slot and with suctionslot at optimum Lss and Dss under unsteady flow with sinusoidal inlet velocity.


11.266 11.734 12.304 13.642 14.406

Without Suction Slot 0.0803 0.0879 0.0931 0.0825 0.0709D =0. 001ss m at L =45%ss 0.1008 0.1019 0.104 0.126 0.094Improvement % 26 16 11 53 32

Fig. 27. The hysteretic behavior due to unsteady flow with sinusoidal inlet velocity atdifferent angles of attack with optimum Lss (45%) and optimum Dss (0.001 m).


44

4.1.3. Second law analysisFig. 24 shows that the suction slot has a negative effect on the

second law efficiency, where the global entropy generation rateincreases at all angles from (14–41%). The 10.6° angle of attack(before the stall) has the highest difference in global entropy generationrate by 41% due to suction slot. On the other hand, 8.7 (before the stall)and 13.6 (after the stall) degree angle of attack have the lowestdifference in global entropy generation rate by 14% due to suctionslot. Otherwise, the 10.1, 11.27, 11.74 and 12.3 (before the stall)degree have the same difference in global entropy generation rate by

21.5% due to suction slot. Also, the 14.4 (after the stall) degree has adifference in the global entropy generation rate by 30%. This phenom-enon suggests that the change in velocity gradient due to the suctionslot has a direct impact on the entropy generation.

4.2. Sinusoidal wave

4.2.1. Torque coefficient and Stall angleFig. 25a) clarifies the instantaneous torque coefficient at compres-

sion cycle for different Lss, while Fig. 25b) shows the average value of

Fig. 28. Torque coefficients at compression cycle for different angles of attack under unsteady flow with sinusoidal inlet velocity with optimum Lss (45%) and optimum Dss (0.001 m), a)

11.3°, b) 11.7°, c) 12.3°, d) 13.6°, e) 14.4°.


45

torque coefficient. These values are at citrine angle of attack of 13.6°and citrine Dss equal to 0.001 m. The Lss equal to 45%, gives a highertorque coefficient value than other Lss. This result is consistent with theresult from previous section. Fig. 26 shows the effect of Lss with 45%and Dss equal to 0.001 m, on torque coefficient at different angles. Theimprovement of torque coefficient is clearly noted before the stallregime (from 11% to 26%) and at stall regime (from 32% to 53%).Table 5 shows more details about the value of improvement in torquecoefficient.

Fig. 27 explains the hysteretic behavior due to the reciprocatingflow, the performance of the Wells turbine has a hysteretic loop inwhich the values of torque coefficient in the accelerating flow is smaller

than in the decelerating flow. The hysteretic behavior was studiedexperimentally and numerically in the Refs. Setoguchi et al. (2003a,2003b, 1998), Mamun (2006), Mamun et al. (2004), Kinoue et al.(2003a, 2004, 2003b), Kim et al. (2002), Thakker and Abdulhadi(2008, 2007). By a numerical simulation using a quasi-steady analysis,it can be that the only study which simulated the hysteretic behaviorafter the stall is Setoguchi et al., (2003a). Moreover, Fig. 27 highlightsthe hysteretic behavior after adding the suction slot to the airfoil whichhas the same behavior. Furthermore, it delays the stall regime inaddition the torque coefficient. The torque coefficients at compressioncycle for different angles of attack are shown in Fig. 28. It can beobserved that for all angles, the suction slot increases the torquecoefficient. Fig. 28d) and e) have the highest increase value in

Fig. 29. Velocity magnitude contours at maximum velocity equal to 2.92 (m/s) forsinusoidal input flow, at 12.3°, before the stall.

Fig. 30. a) and b) Velocity magnitude contours, c) and d) mean velocity magnitude contours, at maximum velocity equal to 2.92 (m/s) for sinusoidal input flow, at 13.6°, after the stall.

Fig. 31. Path-line colored by mean velocity magnitude at maximum velocity equal to2.92 (m/s) for sinusoidal input flow, at 12.3°, before the stall. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of thisarticle.)


46

comparison to other Figures. Whereas, the torque coefficient wasincreased by (approximately) 26% in Fig. 28a), 16% in Fig. 28b) and11% in Fig. 28c). The stall regime was delayed in Fig. 28d), in addition,the torque coefficient was increased by (approximately) 53% and by(approximately) 32% in Fig. 28e). Furthermore, the behavior of torquecoefficient with the suction slot curve was more stable than thatwithout suction slot which is increased from the amount of highestvalue, as it see in Fig. 28d) and e).

4.2.2. Flow field around the airfoil sectionThe flow structures over the NACA0015 airfoil in oscillating flow

was shown in Figs. 29 and 30. Fig. 29 accentuates the contour of

velocity magnitude at maximum velocity and angle of attack equal to12.3° (before the stall). The improvement effect of the suction slot onflow structures is clear when compared between Fig. 29a) and b),especially in, the separated layer regime at the end of airfoil. The samebehavior occurs in Fig. 30a) and b) for the contour of velocitymagnitude, and also in c) and d) for mean velocity magnitude fromunsteady statistics. Fig. 30 emphasize the improvement effect of thesuction slot on flow structures at maximum velocity and angle of attackequal to 13.6° (after the stall). The suction slot has a direct effect on theflow structures at the end of blade, which leads to an improvement inthe separation regime.

The path-lien colored by means of velocity magnitude highlight theimprovement effect of the suction slot on the separation layers inFigs. 31 and 32. It can be noted that by adding the suction slot in theairfoil, this suction slot was decreased from the separation layer at theend of airfoil. By comparing Fig. 31 (before the stall) and Fig. 32 (afterthe stall), it can be also noted that, the improvement effect of suctionslot on separation layers was increased in the stall regime. The pressuredistribution around the upper and lower surface at 12.3° before thestall (Fig. 33) and 13.6° after the stall (Fig. 34) were presented. Theeffect of the suction slot on the trailing edge area was appearingthrough the decrease from the low pressure area that cause distur-bances in the path line at the trailing edge area and it extends to thearea beyond the trailing edge. The pressure distribution after suctionslot location (L =SS 45%) at the upper surface has a direct effect in itsvalue before and after the stall. The difference in pressure valuebetween the upper and lower surface after the slot location (Fig. 34)was decreased due to the slot effect. This decrease made the pressuredistribution behavior similar to the pressure distribution for the uppersurface of the airfoil before the stall (Fig. 33) which led to a delay on thestall condition.

4.2.3. Second law analysisThe numerical simulations are used to obtain local entropy viscosity

Fig. 32. Path-line colored by mean velocity magnitude at maximum velocity equal to2.92 (m/s) for sinusoidal input flow, at 13.6°, after the stall. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of thisarticle.)

Fig. 33. The pressure distribution at maximum velocity equal to 2.92 (m/s) for sinusoidal input flow, at 12.3°, before the stall.


47

predictions of the different angle of attack. Figs. 35 and 36 highlight thesuction slot effect in the entropy behavior when a flow is acceleratingand decelerating in compression cycle. Consequently, the entropygenerations rate varies with the Reynolds number. The change ofReynolds number values results as a consequence to using sinusoidalwave boundary conditions. Suction slot have negative effect on theentropy behavior in both accelerating and decelerating flow. Otherwise,at some Reynolds numbers, the suction slot decreased from the entropygeneration. As an illustration, Fig. 35e) at Reynolds number is less than100000 in accelerating flow. Also, Fig. 36a) at Reynolds number isequal to 160000 in decelerating flow. The airfoil with the suction slot at11.3° has an average increase in the entropy generation rate by 22%than that without the suction slot for the accelerating flow. Whereas, onthe one hand, the maximum difference in the entropy generation ratewas found at Reynolds number to be equal to 193000 and 200000 by36% than that without the suction slot. On the other hand, theminimum difference in the entropy generation rate was found atReynolds number from 50000 to 100000 by 11% than that withoutthe suction slot; see Fig. 35a). For decelerating flow at 11.3°, it can benoted that the maximum increase in the entropy generation rate due tothe suction slot was 35% at Reynolds number equal to 55000.Additionally, on one hand, the entropy generation rate was decreasedthan that without the suction slot by −23% at 160000 Reynoldsnumber. This increase and decrease in the entropy generation ratefor the airfoil with the suction slot gives an average value equal to 0% atdecelerating flow, see Fig. 36a). From Fig. 35b), it can be noted that themaximum increase in the entropy generation rate is 39% due to thesuction slot for accelerating flow at 198000 Reynolds number. On theother hand, the minimum increase in the entropy generation rate is11% at Reynolds number from 78000 to 100000, with an average

percentage 22% for the 11.7°. For decelerating flow at 11.7°, themaximum increase in the entropy generation rate is 31% at 30000Reynolds number and the minimum value is −14% at 175000 Reynoldsnumber, due to the decrease of the entropy generation rate than thatwithout the suction slot. This increase and decrease in the entropygeneration rate for the airfoil with the suction slot gives an averagevalue equal to 14% at decelerating flow, see Fig. 36b). The 12.3° ataccelerating flow gives maximum increase by 35% at 200000 Reynoldsnumber and minimum increase by 6% Reynolds number from 78000 to100000 with an average percentage 21%, see Fig. 35c). Otherwise,Fig. 36c) shows the maximum increase by 34% at 80000 Reynoldsnumber and minimum increase by 3% 160000 Reynolds number withan average percentage 18%.

The airfoil with the suction slot at 13.6° has an average increase inthe entropy generation rate by 51% than that without the suction slotfor the accelerating flow. Whereas, the maximum different in theentropy generation rate was found at Reynolds number to be equal to28400 by 152% than that without suction slot. On the other hand, theminimum difference in the entropy generation rate was found at160000 Reynolds number by 17% than that without the suction slot,see Fig. 35d). For decelerating flow at 13.6°, the maximum increase inthe entropy generation rate is 36% at 160000 Reynolds number and theminimum value is −5% at 80000 Reynolds number, due to the decreaseof the entropy generation rate than that without the suction slot. Thisincrease and decrease in the entropy generation rate for the airfoil withthe suction slot gives an average value equal to 19% at deceleratingflow, see Fig. 36d). The 14.4° at accelerating flow gives maximumincrease by 26% at 185000 and 198000 Reynolds number, andminimum increase by −30% Reynolds number from 54000 to 80000due to the decrease of the entropy generation rate than that without

Fig. 34. The pressure distribution at maximum velocity equal to 2.92 (m/s) for sinusoidal input flow, at 13.6°, after the stall.


48

suction slot. This increase and decrease in the entropy generation ratefor the airfoil with the suction slot gives an average value equal to 3% ataccelerating flow, see Fig. 35e). Otherwise, Fig. 36e) shows themaximum increase by 46% at 80000 and 143000 Reynolds number,and minimum increase by 0% 100000 Reynolds number with anaverage percentage 21%.

Furthermore, as an average value for the compression cycle, thesuction slot was increased from the global entropy generation rate, seeFig. 37. This led to a decrease in the second law efficiency, see Fig. 38.From Figs. 37 and 38, it is deducted that the minimum value for theglobal entropy generation rate and maximum second law efficiencyoccurs at 11.7° for airfoil without the suction slot. On the other hand,the minimum value for the global entropy generation rate andmaximum second law efficiency occurs at 11.3° for airfoil with thesuction slot.

5. Conclusions

A two-dimensional incompressible unsteady flow is simulated forairfoil under different conditions to investigate the effect of airfoil witha suction slot on the torque coefficient and a stall condition as well asthe entropy generation due to viscous dissipation. The modeling resultsshow that Dss and Lss have different effects on the torque coefficient andstall condition. Therefore, not all the parameters tested in the presentstudy achieve a positive effect in terms of improved blade torque. Ingeneral, it can be concluded that the decrease in Dss comes with anincrease in torque coefficient. The smallest tested Dss is 0.001 m, sinceany smaller value would not be practical in real industries. Also, thebest Lss is locating (approximately) at 45% from the leading edge (at13.6°). By applying these conditions we can achieve a 53% increase inthe torque coefficient at stall regime (13.6°). The increase in torque

Fig. 35. The global entropy generation rate variation with different Reynolds number at accelerating flow in compression cycle for different angles of attack with optimum Lss (45%) and

optimum Dss (0.001 m).


49

coefficient, due to the suction slot, ranges from 11% to 26% before thestall regime. Hence, the regime after the stall increases in torquecoefficient varying from 32% to 53%. The main reason behind thisobservation is due to the delay of the stall condition. The suction slotincreases the torque coefficient and delays the stall angle which furtherleads to an increase of first law efficiency. On the other hand, itdecreases the second law efficiency. Thus, if the turbine operates underhigh flow coefficient (angle of attack), it is strongly suggested to use the

suction slot to improve the performance at the stall condition.Otherwise, it may not be effective. Future research should focus onimproving the first law efficiency with a minimize entropy generation,by using numerical algorism and experimental test, in order to enhancethe overall Wells turbine performance under flow control method.Furthermore, it should investigate the suction slot and its location inthe third direction (Z axis) via three-dimensional simulation.

Fig. 36. The global entropy generation rate variation with different Reynolds number at decelerating flow in compression cycle for different angles of attack with optimum Lss (45%) and

optimum Dss (0.001 m).


50

Acknowledgements

The authors would like to acknowledge the support provided by theDepartment of Naval Architecture, Ocean and Marine Engineering atStrathclyde University, UK and the Department of Marine Engineeringat Arab Academy for Science, Technology and Maritime Transport.

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